13 is the standard amount of steps in stairs in houses (in the UK at least). So statistically, you should just go with 13 instead of counting them and you will get it right almost all of the time.
I looked at our stairs at home and they have 13 steps with a rise of what looks like a bit less than 20cm - hard to measure accurately with the carpet. That gives a total height of 2.5m which is nice and round.
A bit of searching around and I find the building regulations permit a rise per step between 15cm and 22cm. And I find a site which says “A typical rise is 2,600mm, which divides easily into 13 200mm risers, or steps”
I roughly measured the overall height of 8 steps and it was closer to 160cm than 152cm so looks like they are the typical dimensions.
I'd wager that when that standard was established the divisivility of those metric measurements would not have been a consideration. Most likely it's also close to some even fraction of feet and inches.
This house dates from about 1990 so I think it is built to modern dimensions, but I know nothing about this so I am mostly guessing... the 19cm ish riser also matches an 8’ floor-to-floor height, so it’s a bit hard to tell from just the stairs :-)
2.5m is 8 foot 2.4 inches according to Google (decimals in measurement that are in inches is a thing? I’m metric so don’t know).
The standard ceiling distance between floors must be 8 feet in the U.K..
The joists and surfaces between floors in a home are 12-14 inches thick in total, bringing the distance between the floor and ceiling in each level closer to 7 feet.
I’ve phrased that badly. Obviously the stairs go floor to floor... wall height would obviously be floor to floor minus joists, flooring, ceiling material.
Reminded me of this video [1] talking about the fact that there are signs in London tube stations claiming the stairs are equivalent to 15 floors, regardless of the number of steps.
The number of floors is roughly correct for Covent Garden, so I guess it's possible that the original typesetter changed the number of steps, but forgot to change the number of floors.
Incidental anecdote: While searching for this video, which I'd seen a year or so ago, I googled "tube 15 floors sign", but didn't see a reference to it, so I opened YouTube instead, and there, in recommended videos, was a video about the tube... by the same person that made the video above. It was a short hop to find the correct video.
It had never occurred to me that Google personalize youtube searches based on your google searches.
I'd imagine since building codes maximum stair rise has been standardized.
So that, plus a limited number of common ceiling heights, results in a few standard numbers of stairs.
Additionally, building to standards allows you to use interchangeable materials [e.g. 1], decreasing onsite time, which usually directly translates into profit. (Labor is expensive)
It seems reasonable the same has generally been true throughout modern history.
